Finite Group Databasebeta

← C11×#18938 #14596131

Subgroups — C11×#18938 #14596131

Order 2816.

892 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3550C211yesmaximal, characteristic, complemented
2C11×#3246C211yesmaximal, characteristic, complemented
3C11×#3216C211yesmaximal, characteristic, complemented
4C11×#3207C211yesmaximal, characteristic
5C11×#1645C212yesmaximal, complemented
6C11×#1640C212yesmaximal, complemented
7C11×#1623C212yesmaximal, complemented
8C11×#1620C212yesmaximal, complemented
9C11×#1551C211yesmaximal, characteristic, complemented
10C11×#1497C211yesmaximal, characteristic, complemented
11C11×#1481C211yesmaximal, characteristic, complemented
12C11×#563—22no—
13C11×#559C2212yes—
14Q82×C11C2212yes—
15C11×#556—21no—
16C11×#556—21no—
17D4×Q8×C11—21no—
18D4×Q8×C11—21no—
19C11×#542—22no—
20C11×#542—22no—
21C11×#536—22no—
22C11×#533C2211yescharacteristic
23C11×#533C2211yescharacteristic
24C11×#532C2211yescharacteristic
25C11×#532C2211yescharacteristic
26C11×#497—21no—
27C11×#493C2211yescharacteristic
28C11×#492C2211yescharacteristic
29C11×#489—21no—
30C11×#487C2211yescharacteristic
31C11×#486C2211yescharacteristic
32C11×#476—21no—
33C11×#475C2212yes—
34C11×#465—22no—
35C11×#463—22no—
36C11×#462C2212yes—
37C11×#461—21no—
38C11×#460C2212yes—
39C11×#460C2212yes—
40C11×#452—22no—
41C11×#449—22no—
42C11×#432C2211yescharacteristic
43C11×#431C2211yescharacteristic
44C2×C11×C4⋊C8C2211yescharacteristic
45C11×#333C2212yes—
46C11×#331C2212yes—
47C11×Q8⋊C8C2212yes—
48C11×Q8⋊C8C2212yes—
49C11×Q8⋊C8C2212yes—
50C11×Q8⋊C8C2212yes—
51C2×C11×#41—21no—
52C2×C11×#41D412yes—
53C22×Q8×C11—22no—
54C2×C11×Q16—22no—
55C2×C11×SD16—22no—
56C2×C11×SD16—22no—
57C2×C11×SD16—22no—
58C2×C11×D8—22no—
59C22×C8×C11—21no—
60C11×C4⋊Q8—24no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8D411yescharacteristic
65C11×C4⋊Q8D411yescharacteristic
66C11×C4⋊Q8D411yescharacteristic
67C11×C4⋊Q8C2311yescharacteristic
68C11×C4⋊Q8C2311yescharacteristic
69C11×#127C2311yescharacteristic
70C11×#127C2311yescharacteristic
71C11×#126—24no—
72C11×#126—24no—
73C11×#125—21no—
74C11×#125—21no—
75C11×#124—24no—
76C11×#124—22no—
77C11×#124—22no—
78C11×#124—21no—
79C11×#124D412yes—
80C11×#123—24no—
81C11×#123—24no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—24no—
85C11×C22⋊Q8—24no—
86C11×C22⋊Q8—21no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8D412yes—
89C11×C22⋊Q8D412yes—
90C11×#121—21no—
91C11×#121—21no—
92C11×#121—21no—
93C11×#121—21no—
94C4×Q8×C11—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11—21no—
97C4×Q8×C11—21no—
98C4×Q8×C11C2312yes—
99C4×Q8×C11C2312yes—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11—21no—
106C11×#117—22no—
107C11×#117—21no—
108C11×#117—21no—
109C2×C42×C11C2311yescharacteristic
110C11×#106—22no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8C2312yes—
114C11×C4⋊C8C2312yes—
115C11×#103—22no—
116C11×#103—22no—
117C11×#103—22no—
118C11×#102—22no—
119C11×#102—22no—
120C11×#102—22no—
121C11×C22⋊C8—21no—
122C11×C22⋊C8—21no—
123C11×#97—21no—
124C4×C8×C11C2311yescharacteristic
125C4×C8×C11C2311yescharacteristic
126#18938C1111yesmaximal, characteristic, direct product factor, Sylow
127C11×#41—82no—
128C11×#41—82no—
129C2×Q8×C11—24no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—84no—
134C2×Q8×C11C2×D412yes—
135C2×Q8×C11C2×D412yes—
136C2×Q8×C11C2×D412yes—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—41no—
144C2×D4×C11C2×D412yes—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—41no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C11×Q16—82no—
152C11×SD16—82no—
153C11×SD16—82no—
154C11×SD16—82no—
155C11×D8—82no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—81no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C2×D412yes—
178C11×C4⋊C4C2×D412yes—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—41no—
187C11×C22⋊C4—41no—
188C42×C11—24no—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11C2411yescharacteristic
195#3550C2×C1111yescharacteristic, complemented
196#3246C2×C1111yescharacteristic, complemented
197#3216C2×C1111yescharacteristic, complemented
198#3207C2×C1111yescharacteristic
199#1645C2×C1112yescomplemented
200#1640C2×C1112yescomplemented
201#1623C2×C1112yescomplemented
202#1620C2×C1112yescomplemented
203#1551C2×C1111yescharacteristic, complemented
204#1497C2×C1111yescharacteristic, complemented
205#1481C2×C1111yescharacteristic, complemented
206C23×C11—22no—
207C23×C11—41no—
208C23×C11#12011yescharacteristic
209Q8×C11—22no—
210Q8×C11—22no—
211Q8×C11—22no—
212Q8×C11—22no—
213Q8×C11—42no—
214Q8×C11—42no—
215Q8×C11—42no—
216Q8×C11—42no—
217Q8×C11—84no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—42no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11—82no—
227D4×C11—82no—
228C2×C4×C11—21no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—41no—
237C2×C4×C11—44no—
238C2×C4×C11—41no—
239C2×C4×C11—82no—
240C2×C4×C11—84no—
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11#12011yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C8×C11—41no—
248C8×C11—41no—
249C8×C11—42no—
250C8×C11—42no—
251#563—22no—
252#559C22×C1112yes—
253Q82C22×C1112yes—
254#556—21no—
255#556—21no—
256D4×Q8—21no—
257D4×Q8—21no—
258#542—22no—
259#542—22no—
260#536—22no—
261#533C22×C1111yescharacteristic
262#533C22×C1111yescharacteristic
263#532C22×C1111yescharacteristic
264#532C22×C1111yescharacteristic
265#497—21no—
266#493C22×C1111yescharacteristic
267#492C22×C1111yescharacteristic
268#489—21no—
269#487C22×C1111yescharacteristic
270#486C22×C1111yescharacteristic
271#476—21no—
272#475C22×C1112yes—
273#465—22no—
274#463—22no—
275#462C22×C1112yes—
276#461—21no—
277#460C22×C1112yes—
278#460C22×C1112yes—
279#452—22no—
280#449—22no—
281#432C22×C1111yescharacteristic
282#431C22×C1111yescharacteristic
283C2×C4⋊C8C22×C1111yescharacteristic
284#333C22×C1112yes—
285#331C22×C1112yes—
286Q8⋊C8C22×C1112yes—
287Q8⋊C8C22×C1112yes—
288Q8⋊C8C22×C1112yes—
289Q8⋊C8C22×C1112yes—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11C2×#12011yescharacteristic
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—81no—
310C4×C11#57712yes—
311C4×C11#57711yescharacteristic
312C4×C11#57811yescharacteristic
313C2×#41—21no—
314C2×#41D4×C1112yes—
315C22×Q8—22no—
316C2×Q16—22no—
317C2×SD16—22no—
318C2×SD16—22no—
319C2×SD16—22no—
320C2×D8—22no—
321C22×C8—21no—
322C4⋊Q8—24no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8D4×C1111yescharacteristic
326C4⋊Q8D4×C1111yescharacteristic
327C4⋊Q8D4×C1111yescharacteristic
328C4⋊Q8D4×C1111yescharacteristic
329C4⋊Q8C23×C1111yescharacteristic
330C4⋊Q8C23×C1111yescharacteristic
331#127C23×C1111yescharacteristic
332#127C23×C1111yescharacteristic
333#126—24no—
334#126—24no—
335#125—21no—
336#125—21no—
337#124—24no—
338#124—22no—
339#124—22no—
340#124—21no—
341#124D4×C1112yes—
342#123—24no—
343#123—24no—
344C22⋊Q8—22no—
345C22⋊Q8—22no—
346C22⋊Q8—24no—
347C22⋊Q8—24no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8D4×C1112yes—
351C22⋊Q8D4×C1112yes—
352#121—21no—
353#121—21no—
354#121—21no—
355#121—21no—
356C4×Q8—22no—
357C4×Q8—22no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8C23×C1112yes—
361C4×Q8C23×C1112yes—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4—21no—
368#117—22no—
369#117—21no—
370#117—21no—
371C2×C42C23×C1111yescharacteristic
372#106—22no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8C23×C1112yes—
376C4⋊C8C23×C1112yes—
377#103—22no—
378#103—22no—
379#103—22no—
380#102—22no—
381#102—22no—
382#102—22no—
383C22⋊C8—21no—
384C22⋊C8—21no—
385#97—21no—
386C4×C8C23×C1111yescharacteristic
387C4×C8C23×C1111yescharacteristic
388C2×C11—41no—
389C2×C11—82no—
390C2×C11—161no—
391C2×C11#301011yescharacteristic
392C2×C11#301311yescharacteristic
393C2×C11#301911yescharacteristic
394#41—82no—
395#41—82no—
396C2×Q8—24no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—84no—
401C2×Q8C2×D4×C1112yes—
402C2×Q8C2×D4×C1112yes—
403C2×Q8C2×D4×C1112yes—
404C2×D4—22no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—41no—
411C2×D4C2×D4×C1112yes—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—41no—
415C22×C4C2×D4×C1111yescharacteristic
416C22×C4C2×D4×C1111yescharacteristic
417C22×C4C2×D4×C1111yescharacteristic
418Q16—82no—
419SD16—82no—
420SD16—82no—
421SD16—82no—
422D8—82no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—81no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4C2×D4×C1112yes—
445C4⋊C4C2×D4×C1112yes—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—41no—
454C22⋊C4—41no—
455C42—24no—
456C42—22no—
457C42—22no—
458C42C2×D4×C1111yescharacteristic
459C42C2×D4×C1111yescharacteristic
460C42C2×D4×C1111yescharacteristic
461C42C24×C1111yescharacteristic
462C11#1893811yescharacteristic, direct product factor, Sylow
463C23—22no—
464C23—41no—
465C23C11×#12011yescharacteristic
466Q8—22no—
467Q8—22no—
468Q8—22no—
469Q8—22no—
470Q8—42no—
471Q8—42no—
472Q8—42no—
473Q8—42no—
474Q8—84no—
475D4—42no—
476D4—42no—
477D4—42no—
478D4—41no—
479D4—41no—
480D4—42no—
481D4—41no—
482D4—41no—
483D4—82no—
484D4—82no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—41no—
494C2×C4—44no—
495C2×C4—41no—
496C2×C4—82no—
497C2×C4—84no—
498C2×C4C11×#12011yescharacteristic
499C2×C4C11×#12011yescharacteristic
500C2×C4C11×#12011yescharacteristic
501C2×C4C22×D4×C1111yescharacteristic
502C2×C4C22×D4×C1111yescharacteristic
503C2×C4C22×D4×C1111yescharacteristic
504C8—41no—
505C8—41no—
506C8—42no—
507C8—42no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22C2×C11×#12011yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—81no—
528C4C11×#57712yes—
529C4C11×#57711yescharacteristic
530C4C11×#57811yescharacteristic
531C2—41no—
532C2—82no—
533C2—161no—
534C2C11×#301011yescharacteristic
535C2C11×#301311yescharacteristic
536C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3207C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#3550C2semidirect
2. C11×#3246C2semidirect
3. C11×#3216C2semidirect
5. C11×#1645C2semidirect
6. C11×#1640C2semidirect
7. C11×#1623C2semidirect
8. C11×#1620C2semidirect
9. C11×#1551C2semidirect
10. C11×#1497C2semidirect
11. C11×#1481C2semidirect
126. #18938C11direct (N × H)
195. #3550C2×C11semidirect
196. #3246C2×C11semidirect
197. #3216C2×C11semidirect
199. #1645C2×C11semidirect
200. #1640C2×C11semidirect
201. #1623C2×C11semidirect
202. #1620C2×C11semidirect
203. #1551C2×C11semidirect
204. #1497C2×C11semidirect
205. #1481C2×C11semidirect
462. C11#18938direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#35502
C11×#32462
C11×#32162
C11×#32072
C11×#16452
C11×#16402
C11×#16232
C11×#16202
C11×#15512
C11×#14972
C11×#14812
#1893811